/****************************************************************************
 *
 * Copyright 2018 Samsung Electronics All Rights Reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND,
 * either express or implied. See the License for the specific
 * language governing permissions and limitations under the License.
 *
 ****************************************************************************/
/****************************************************************************
 * libc/math/lib_gamma.c
 *
 * Ported to NuttX from FreeBSD by Alan Carvalho de Assis:
 *
 *   Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 *   Developed at SunSoft, a Sun Microsystems, Inc. business.
 *   Permission to use, copy, modify, and distribute this
 *   software is freely granted, provided that this notice
 *   is preserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 * 3. Neither the name NuttX nor the names of its contributors may be
 *    used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
 * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
 * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 ****************************************************************************/

/* lgamma_r(x, signgamp)
 *
 * Reentrant version of the logarithm of the Gamma function
 * with user provide pointer for the sign of Gamma(x).
 *
 * Method:
 *   1. Argument Reduction for 0 < x <= 8
 *      Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
 *      reduce x to a number in [1.5,2.5] by
 *              lgamma(1+s) = log(s) + lgamma(s)
 *      for example,
 *              lgamma(7.3) = log(6.3) + lgamma(6.3)
 *                          = log(6.3*5.3) + lgamma(5.3)
 *                          = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
 *   2. Polynomial approximation of lgamma around its
 *      minimun ymin=1.461632144968362245 to maintain monotonicity.
 *      On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
 *              Let z = x-ymin;
 *              lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
 *      where
 *              poly(z) is a 14 degree polynomial.
 *   2. Rational approximation in the primary interval [2,3]
 *      We use the following approximation:
 *              s = x-2.0;
 *              lgamma(x) = 0.5*s + s*P(s)/Q(s)
 *      with accuracy
 *              |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
 *      Our algorithms are based on the following observation
 *
 *                             zeta(2)-1    2    zeta(3)-1    3
 * lgamma(2+s) = s*(1-Euler) + --------- * s  -  --------- * s  + ...
 *                                 2                 3
 *
 *      where Euler = 0.5771... is the Euler constant, which is very
 *      close to 0.5.
 *
 *   3. For x>=8, we have
 *      lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
 *      (better formula:
 *         lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
 *      Let z = 1/x, then we approximation
 *              f(z) = lgamma(x) - (x-0.5)(log(x)-1)
 *      by
 *                                  3       5             11
 *              w = w0 + w1*z + w2*z  + w3*z  + ... + w6*z
 *      where
 *              |w - f(z)| < 2**-58.74
 *
 *   4. For negative x, since (G is gamma function)
 *              -x*G(-x)*G(x) = pi/sin(pi*x),
 *      we have
 *              G(x) = pi/(sin(pi*x)*(-x)*G(-x))
 *      since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
 *      Hence, for x<0, signgam = sign(sin(pi*x)) and
 *              lgamma(x) = log(|Gamma(x)|)
 *                        = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
 *      Note: one should avoid compute pi*(-x) directly in the
 *            computation of sin(pi*(-x)).
 *
 *   5. Special Cases
 *              lgamma(2+s) ~ s*(1-Euler) for tiny s
 *              lgamma(1) = lgamma(2) = 0
 *              lgamma(x) ~ -log(|x|) for tiny x
 *              lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero
 *              lgamma(inf) = inf
 *              lgamma(-inf) = inf (bug for bug compatible with C99!?)
 */

/****************************************************************************
 * Included Files
 ****************************************************************************/

#include <tinyara/config.h>
#include <tinyara/compiler.h>

#include <sys/types.h>
#include <math.h>

#ifdef CONFIG_HAVE_DOUBLE

/****************************************************************************
 * Private Data
 ****************************************************************************/

static int g_signgam = 0;

static const double g_pi = 3.14159265358979311600e+00;	/* 0x400921FB, 0x54442D18 */
static const double g_a0 = 7.72156649015328655494e-02;	/* 0x3FB3C467, 0xE37DB0C8 */
static const double g_a1 = 3.22467033424113591611e-01;	/* 0x3FD4A34C, 0xC4A60FAD */
static const double g_a2 = 6.73523010531292681824e-02;	/* 0x3FB13E00, 0x1A5562A7 */
static const double g_a3 = 2.05808084325167332806e-02;	/* 0x3F951322, 0xAC92547B */
static const double g_a4 = 7.38555086081402883957e-03;	/* 0x3F7E404F, 0xB68FEFE8 */
static const double g_a5 = 2.89051383673415629091e-03;	/* 0x3F67ADD8, 0xCCB7926B */
static const double g_a6 = 1.19270763183362067845e-03;	/* 0x3F538A94, 0x116F3F5D */
static const double g_a7 = 5.10069792153511336608e-04;	/* 0x3F40B6C6, 0x89B99C00 */
static const double g_a8 = 2.20862790713908385557e-04;	/* 0x3F2CF2EC, 0xED10E54D */
static const double g_a9 = 1.08011567247583939954e-04;	/* 0x3F1C5088, 0x987DFB07 */
static const double g_a10 = 2.52144565451257326939e-05;	/* 0x3EFA7074, 0x428CFA52 */
static const double g_a11 = 4.48640949618915160150e-05;	/* 0x3F07858E, 0x90A45837 */
static const double g_tc = 1.46163214496836224576e+00;	/* 0x3FF762D8, 0x6356BE3F */
static const double g_tf = -1.21486290535849611461e-01;	/* 0xBFBF19B9, 0xBCC38A42 */

/* tt = -(tail of tf) */

static const double g_tt = -3.63867699703950536541e-18;	/* 0xBC50C7CA, 0xA48A971F */
static const double g_t0 = 4.83836122723810047042e-01;	/* 0x3FDEF72B, 0xC8EE38A2 */
static const double g_t1 = -1.47587722994593911752e-01;	/* 0xBFC2E427, 0x8DC6C509 */
static const double g_t2 = 6.46249402391333854778e-02;	/* 0x3FB08B42, 0x94D5419B */
static const double g_t3 = -3.27885410759859649565e-02;	/* 0xBFA0C9A8, 0xDF35B713 */
static const double g_t4 = 1.79706750811820387126e-02;	/* 0x3F9266E7, 0x970AF9EC */
static const double g_t5 = -1.03142241298341437450e-02;	/* 0xBF851F9F, 0xBA91EC6A */
static const double g_t6 = 6.10053870246291332635e-03;	/* 0x3F78FCE0, 0xE370E344 */
static const double g_t7 = -3.68452016781138256760e-03;	/* 0xBF6E2EFF, 0xB3E914D7 */
static const double g_t8 = 2.25964780900612472250e-03;	/* 0x3F6282D3, 0x2E15C915 */
static const double g_t9 = -1.40346469989232843813e-03;	/* 0xBF56FE8E, 0xBF2D1AF1 */
static const double g_t10 = 8.81081882437654011382e-04;	/* 0x3F4CDF0C, 0xEF61A8E9 */
static const double g_t11 = -5.38595305356740546715e-04;	/* 0xBF41A610, 0x9C73E0EC */
static const double g_t12 = 3.15632070903625950361e-04;	/* 0x3F34AF6D, 0x6C0EBBF7 */
static const double g_t13 = -3.12754168375120860518e-04;	/* 0xBF347F24, 0xECC38C38 */
static const double g_t14 = 3.35529192635519073543e-04;	/* 0x3F35FD3E, 0xE8C2D3F4 */
static const double g_u0 = -7.72156649015328655494e-02;	/* 0xBFB3C467, 0xE37DB0C8 */
static const double g_u1 = 6.32827064025093366517e-01;	/* 0x3FE4401E, 0x8B005DFF */
static const double g_u2 = 1.45492250137234768737e+00;	/* 0x3FF7475C, 0xD119BD6F */
static const double g_u3 = 9.77717527963372745603e-01;	/* 0x3FEF4976, 0x44EA8450 */
static const double g_u4 = 2.28963728064692451092e-01;	/* 0x3FCD4EAE, 0xF6010924 */
static const double g_u5 = 1.33810918536787660377e-02;	/* 0x3F8B678B, 0xBF2BAB09 */
static const double g_v1 = 2.45597793713041134822e+00;	/* 0x4003A5D7, 0xC2BD619C */
static const double g_v2 = 2.12848976379893395361e+00;	/* 0x40010725, 0xA42B18F5 */
static const double g_v3 = 7.69285150456672783825e-01;	/* 0x3FE89DFB, 0xE45050AF */
static const double g_v4 = 1.04222645593369134254e-01;	/* 0x3FBAAE55, 0xD6537C88 */
static const double g_v5 = 3.21709242282423911810e-03;	/* 0x3F6A5ABB, 0x57D0CF61 */
static const double g_s0 = -7.72156649015328655494e-02;	/* 0xBFB3C467, 0xE37DB0C8 */
static const double g_s1 = 2.14982415960608852501e-01;	/* 0x3FCB848B, 0x36E20878 */
static const double g_s2 = 3.25778796408930981787e-01;	/* 0x3FD4D98F, 0x4F139F59 */
static const double g_s3 = 1.46350472652464452805e-01;	/* 0x3FC2BB9C, 0xBEE5F2F7 */
static const double g_s4 = 2.66422703033638609560e-02;	/* 0x3F9B481C, 0x7E939961 */
static const double g_s5 = 1.84028451407337715652e-03;	/* 0x3F5E26B6, 0x7368F239 */
static const double g_s6 = 3.19475326584100867617e-05;	/* 0x3F00BFEC, 0xDD17E945 */
static const double g_r1 = 1.39200533467621045958e+00;	/* 0x3FF645A7, 0x62C4AB74 */
static const double g_r2 = 7.21935547567138069525e-01;	/* 0x3FE71A18, 0x93D3DCDC */
static const double g_r3 = 1.71933865632803078993e-01;	/* 0x3FC601ED, 0xCCFBDF27 */
static const double g_r4 = 1.86459191715652901344e-02;	/* 0x3F9317EA, 0x742ED475 */
static const double g_r5 = 7.77942496381893596434e-04;	/* 0x3F497DDA, 0xCA41A95B */
static const double g_r6 = 7.32668430744625636189e-06;	/* 0x3EDEBAF7, 0xA5B38140 */
static const double g_w0 = 4.18938533204672725052e-01;	/* 0x3FDACFE3, 0x90C97D69 */
static const double g_w1 = 8.33333333333329678849e-02;	/* 0x3FB55555, 0x5555553B */
static const double g_w2 = -2.77777777728775536470e-03;	/* 0xBF66C16C, 0x16B02E5C */
static const double g_w3 = 7.93650558643019558500e-04;	/* 0x3F4A019F, 0x98CF38B6 */
static const double g_w4 = -5.95187557450339963135e-04;	/* 0xBF4380CB, 0x8C0FE741 */
static const double g_w5 = 8.36339918996282139126e-04;	/* 0x3F4B67BA, 0x4CDAD5D1 */
static const double g_w6 = -1.63092934096575273989e-03;	/* 0xBF5AB89D, 0x0B9E43E4 */

/****************************************************************************
 * Private Functions
 ****************************************************************************/

/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */

static double sin_pi(double x)
{
	int n;

	/* spurious inexact if odd int */

	x = 2.0 * (x * 0.5 - floor(x * 0.5));	/* x mod 2.0 */

	n = (int)(x * 4.0);
	n = (n + 1) / 2;
	x -= n * 0.5f;
	x *= g_pi;

	switch (n) {
	default:					/* case 4: */
	case 0:
		return __sin(x, 0.0, 0);

	case 1:
		return __cos(x, 0.0);

	case 2:
		return __sin(-x, 0.0, 0);

	case 3:
		return -__cos(x, 0.0);
	}
}

/****************************************************************************
 * Public Functions
 ****************************************************************************/

double lgamma_r(double x, int *signgamp)
{
	union {
		double f;
		uint64_t i;
	} u;
	u.f = x;

	double t;
	double y;
	double z;
	double nadj = 0.0;
	double p;
	double p1;
	double p2;
	double p3;
	double q;
	double r;
	double w;
	uint32_t ix;
	int sign;
	int i;

	/* purge off +-inf, NaN, +-0, tiny and negative arguments */

	*signgamp = 1;
	sign = u.i >> 63;

	ix = u.i >> 32 & 0x7fffffff;
	if (ix >= 0x7ff00000) {
		return x * x;
	}

	/* |x|<2**-70, return -log(|x|) */

	if (ix < (0x3ff - 70) << 20) {
		if (sign) {
			x = -x;
			*signgamp = -1;
		}
		return -log(x);
	}

	if (sign) {
		x = -x;
		t = sin_pi(x);

		if (t == 0.0) {
			/* -integer */
			return 1.0 / (x - x);
		}

		if (t > 0.0) {
			*signgamp = -1;
		} else {
			t = -t;
		}

		nadj = log(g_pi / (t * x));
	}

	/* purge off 1 and 2 */

	if ((ix == 0x3ff00000 || ix == 0x40000000) && (uint32_t)u.i == 0) {
		r = 0;
	} else {					/* for x < 2.0 */

		if (ix < 0x40000000) {
			if (ix <= 0x3feccccc) {
				/* lgamma(x) = lgamma(x+1)-log(x) */

				r = -log(x);

				if (ix >= 0x3FE76944) {
					y = 1.0 - x;
					i = 0;
				} else {
					if (ix >= 0x3FCDA661) {
						y = x - (g_tc - 1.0);
						i = 1;
					} else {
						y = x;
						i = 2;
					}
				}
			} else {
				r = 0.0;

				if (ix >= 0x3FFBB4C3) {
					/* [1.7316,2] */
					y = 2.0 - x;
					i = 0;
				} else {
					if (ix >= 0x3FF3B4C4) {
						/* [1.23,1.73] */
						y = x - g_tc;
						i = 1;
					} else {
						y = x - 1.0;
						i = 2;
					}
				}
			}

			switch (i) {
			case 0:
				z = y * y;
				p1 = g_a0 + z * (g_a2 + z * (g_a4 + z * (g_a6 + z * (g_a8 + z * g_a10))));
				p2 = z * (g_a1 + z * (g_a3 + z * (g_a5 + z * (g_a7 + z * (g_a9 + z * g_a11)))));
				p = y * p1 + p2;
				r += (p - 0.5 * y);
				break;

			case 1:
				z = y * y;
				w = z * y;
				p1 = g_t0 + w * (g_t3 + w * (g_t6 + w * (g_t9 + w * g_t12)));	/* parallel comp */
				p2 = g_t1 + w * (g_t4 + w * (g_t7 + w * (g_t10 + w * g_t13)));
				p3 = g_t2 + w * (g_t5 + w * (g_t8 + w * (g_t11 + w * g_t14)));
				p = z * p1 - (g_tt - w * (p2 + y * p3));
				r += g_tf + p;
				break;

			case 2:
				p1 = y * (g_u0 + y * (g_u1 + y * (g_u2 + y * (g_u3 + y * (g_u4 + y * g_u5)))));
				p2 = 1.0 + y * (g_v1 + y * (g_v2 + y * (g_v3 + y * (g_v4 + y * g_v5))));
				r += -0.5 * y + p1 / p2;
			}
		} else {
			if (ix < 0x40200000) {
				/* x < 8.0 */

				i = (int)x;
				y = x - (double)i;
				p = y * (g_s0 + y * (g_s1 + y * (g_s2 + y * (g_s3 + y * (g_s4 + y * (g_s5 + y * g_s6))))));
				q = 1.0 + y * (g_r1 + y * (g_r2 + y * (g_r3 + y * (g_r4 + y * (g_r5 + y * g_r6)))));
				r = 0.5 * y + p / q;
				z = 1.0;

				/* lgamma(1+s) = log(s) + lgamma(s) */

				switch (i) {
				case 7:
					z *= y + 6.0;	/* FALLTHRU */
				case 6:
					z *= y + 5.0;	/* FALLTHRU */
				case 5:
					z *= y + 4.0;	/* FALLTHRU */
				case 4:
					z *= y + 3.0;	/* FALLTHRU */
				case 3:
					z *= y + 2.0;	/* FALLTHRU */
					r += log(z);
					break;
				}
			} else {
				if (ix < 0x43900000) {
					/* 8.0 <= x < 2**58 */

					t = log(x);
					z = 1.0 / x;
					y = z * z;
					w = g_w0 + z * (g_w1 + y * (g_w2 + y * (g_w3 + y * (g_w4 + y * (g_w5 + y * g_w6)))));
					r = (x - 0.5) * (t - 1.0) + w;
				} else {
					/* 2**58 <= x <= inf */

					r = x * (log(x) - 1.0);
				}
			}
		}
	}

	if (sign) {
		r = nadj - r;
	}

	return r;
}

double lgamma(double x)
{
	return lgamma_r(x, &g_signgam);
}
#endif
